donkey's years

1923, from donkey's ears, which is rhyming slang for years.[1] That is, donkey's ears is rhyming slang, replacing years with ears, while donkey's years reverts to years, with donkey acting as emphasis. “Donkey’s ears” implies “a long time” because donkey’s ears are long, while “donkey’s years” is supported by the belief that donkeys live a long time.[1]

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donkey's years pl (plural only)

1. (Britain, Ireland, Australia, idiomatic) A long time, years and years.
   • 1923, The Bridgeport Telegram:[1]

     With a heavy make-up, you’ll be the cutest vamp I’ve seen in donkey’s years.

• Michael Quinion (April 15, 2000), “Donkey’s years”, in World Wide Words.